The Church of the Flying Saucer follows Carol Klodie, a former film school student who has hit a slump in her life.
By happenstance, she finds a pamphlet under the windshield of her car advertising what seems to be a support group for UFO abductees and alien conspiracy theorists. She finds the pamphlet ridiculous and intriguing, and begins making a pseudo-documentary about the group, who are known as the Hadrian Burns Association.